Negatively-refractive focusing and sensing apparatus, methods, and systems

ABSTRACT

Apparatus, methods, and systems provide negatively-refractive focusing and sensing of electromagnetic energy. In some approaches the negatively-refractive focusing includes providing an interior focusing region with an axial magnification substantially less than one. In some approaches the negatively-refractive focusing includes negatively-refractive focusing with a transformation medium, where the transformation medium may include an artificially-structured material such as a metamaterial.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is related to and claims the benefit of theearliest available effective filing date(s) from the following listedapplication(s) (the “Related Applications”) (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 USC §119(e) for provisional patentapplications, for any and all parent, grandparent, great-grandparent,etc. applications of the Related Application(s)).

RELATED APPLICATIONS

For purposes of the USPTO extra-statutory requirements, the presentapplication constitutes a continuation-in-part of U.S. patentapplication Ser. No. 12/156,443, entitled FOCUSING AND SENSINGAPPARATUS, METHODS, AND SYSTEMS, naming Jeffrey A. Bowers, Roderick A.Hyde, Edward K. Y. Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T. Tegreene, Thomas A. Weaver, Charles Whitmer, andLowell L. Wood, Jr. as inventors, filed May 30, 2008, which is currentlyco-pending, or is an application of which a currently co-pendingapplication is entitled to the benefit of the filing date.

For purposes of the USPTO extra-statutory requirements, the presentapplication constitutes a continuation-in-part of U.S. patentapplication Ser. No. 12/214,534, entitled EMITTING AND FOCUSINGAPPARATUS, METHODS, AND SYSTEMS, naming Jeffrey A. Bowers, Roderick A.Hyde, Edward K. Y. Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T. Tegreene, Thomas A. Weaver, Charles Whitmer, andLowell L. Wood, Jr. as inventors, filed Jun. 18, 2008, which iscurrently co-pending, or is an application of which a currentlyco-pending application is entitled to the benefit of the filing date.

For purposes of the USPTO extra-statutory requirements, the presentapplication constitutes a continuation-in-part of U.S. patentapplication Ser. No. 12/220,703, entitled EMITTING ANDNEGATIVELY-REFRACTIVE FOCUSING APPARATUS, METHODS, AND SYSTEMS, namingJeffrey A. Bowers, Roderick A. Hyde, Edward K. Y. Jung, John BrianPendry, David Schurig, David R. Smith, Clarence T. Tegreene, Thomas A.Weaver, Charles Whitmer, and Lowell L. Wood, Jr. as inventors, filedJul. 25, 2008, which is currently co-pending, or is an application ofwhich a currently co-pending application is entitled to the benefit ofthe filing date.

For purposes of the USPTO extra-statutory requirements, the presentapplication constitutes a continuation-in-part of U.S. patentapplication Ser. No. 12/220,705, entitled NEGATIVELY-REFRACTIVE FOCUSINGAND SENSING APPARATUS, METHODS, AND SYSTEMS, naming Jeffrey A. Bowers,Roderick A. Hyde, Edward K. Y. Jung, John Brian Pendry, David Schurig,David R. Smith, Clarence T. Tegreene, Thomas A. Weaver, Charles Whitmer,and Lowell L. Wood, Jr. as inventors, filed Jul. 25, 2008, which iscurrently co-pending, or is an application of which a currentlyco-pending application is entitled to the benefit of the filing date.

The United States Patent Office (USPTO) has published a notice to theeffect that the USPTO's computer programs require that patent applicantsreference both a serial number and indicate whether an application is acontinuation or continuation-in-part. Stephen G. Kunin, Benefit ofPrior-Filed Application, USPTO Official Gazette Mar. 18, 2003, availableat http://www.uspto.gov/web/offices/com/sol/og/2003/week11/patbene.htm.The present Applicant Entity (hereinafter “Applicant”) has providedabove a specific reference to the application(s) from which priority isbeing claimed as recited by statute. Applicant understands that thestatute is unambiguous in its specific reference language and does notrequire either a serial number or any characterization, such as“continuation” or “continuation-in-part,” for claiming priority to U.S.patent applications. Notwithstanding the foregoing, Applicantunderstands that the USPTO's computer programs have certain data entryrequirements, and hence Applicant is designating the present applicationas a continuation-in-part of its parent applications as set forth above,but expressly points out that such designations are not to be construedin any way as any type of commentary and/or admission as to whether ornot the present application contains any new matter in addition to thematter of its parent application(s).

All subject matter of the Related Applications and of any and allparent, grandparent, great-grandparent, etc. applications of the RelatedApplications is incorporated herein by reference to the extent suchsubject matter is not inconsistent herewith.

TECHNICAL FIELD

The application discloses apparatus, methods, and systems that mayrelate to electromagnetic responses that include negatively-refractivefocusing and sensing of electromagnetic energy.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 depicts a first configuration of a negatively-refractive focusingstructure.

FIG. 2 depicts a first coordinate transformation.

FIG. 3 depicts a second configuration of a negatively-refractivefocusing structure.

FIG. 4 depicts a second coordinate transformation.

FIG. 5 depicts a negatively-refractive focusing structure with an inputsurface region.

FIG. 6 depicts a first process flow.

FIG. 7 depicts a second process flow.

FIG. 8 depicts a system that includes a focusing unit and a controller.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here.

Transformation optics is an emerging field of electromagneticengineering. Transformation optics devices include lenses that refractelectromagnetic waves, where the refraction imitates the bending oflight in a curved coordinate space (a “transformation” of a flatcoordinate space), e.g. as described in A. J. Ward and J. B. Pendry,“Refraction and geometry in Maxwell's equations,” J. Mod. Optics 43, 773(1996), J. B. Pendry and S. A. Ramakrishna, “Focusing light usingnegative refraction,” J. Phys. [Cond. Matt.] 15, 6345 (2003), D. Schuriget al, “Calculation of material properties and ray tracing intransformation media,” Optics Express 14, 9794 (2006) (“D. Schurig et al(1)”), and in U. Leonhardt and T. G. Philbin, “General relativity inelectrical engineering,” New J. Phys. 8, 247 (2006), each of which isherein incorporated by reference. The use of the term “optics” does notimply any limitation with regards to wavelength; a transformation opticsdevice may be operable in wavelength bands that range from radiowavelengths to visible wavelengths.

A first exemplary transformation optics device is the electromagneticcloak that was described, simulated, and implemented, respectively, inJ. B. Pendry et al, “Controlling electromagnetic waves,” Science 312,1780 (2006); S. A. Cummer et al, “Full-wave simulations ofelectromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006);and D. Schurig et al, “Metamaterial electromagnetic cloak at microwavefrequencies,” Science 314, 977 (2006) (“D. Schurig et al (2)”); each ofwhich is herein incorporated by reference. See also J. Pendry et al,“Electromagnetic cloaking method,” U.S. patent application Ser. No.11/459,728, herein incorporated by reference. For the electromagneticcloak, the curved coordinate space is a transformation of a flat spacethat has been punctured and stretched to create a hole (the cloakedregion), and this transformation corresponds to a set of constitutiveparameters (electric permittivity and magnetic permeability) for atransformation medium wherein electromagnetic waves are refracted aroundthe hole in imitation of the curved coordinate space.

A second exemplary transformation optics device is illustrated byembodiments of the electromagnetic compression structure described in J.B. Pendry, D. Schurig, and D. R. Smith, “Electromagnetic compressionapparatus, methods, and systems,” U.S. patent application Ser. No.11/982,353; and in J. B. Pendry, D. Schurig, and D. R. Smith,“Electromagnetic compression apparatus, methods, and systems,” U.S.patent application Ser. No. 12/069,170; each of which is hereinincorporated by reference. In embodiments described therein, anelectromagnetic compression structure includes a transformation mediumwith constitutive parameters corresponding to a coordinatetransformation that compresses a region of space intermediate first andsecond spatial locations, the effective spatial compression beingapplied along an axis joining the first and second spatial locations.The electromagnetic compression structure thereby provides an effectiveelectromagnetic distance between the first and second spatial locationsgreater than a physical distance between the first and second spatiallocations.

A third exemplary transform optics device is illustrated by embodimentsof the electromagnetic cloaking and/or translation structure describedin J. T. Kare, “Electromagnetic cloaking apparatus, methods, andsystems,” U.S. patent application Ser. No. 12/074,247; and in J. T.Kare, “Electromagnetic cloaking apparatus, methods, and systems,” U.S.patent application Ser. No. 12/074,248; each of which is hereinincorporated by reference. In embodiments described therein, anelectromagnetic translation structure includes a transformation mediumthat provides an apparent location of an electromagnetic transducerdifferent then an actual location of the electromagnetic transducer,where the transformation medium has constitutive parameterscorresponding to a coordinate transformation that maps the actuallocation to the apparent location. Alternatively or additionally,embodiments include an electromagnetic cloaking structure operable todivert electromagnetic radiation around an obstruction in a field ofregard of the transducer (and the obstruction can be anothertransducer).

Additional exemplary transformation optics devices are described in D.Schurig et al, “Transformation-designed optical elements,” Opt. Exp. 15,14772 (2007); M. Rahm et al, “Optical design of reflectionless complexmedia by finite embedded coordinate transformations,” Phys. Rev. Lett.100, 063903 (2008); and A. Kildishev and V. Shalaev, “Engineering spacefor light via transformation optics,” Opt. Lett. 33, 43 (2008); each ofwhich is herein incorporated by reference.

In general, for a selected coordinate transformation, a transformationmedium can be identified wherein electromagnetic waves refract as ifpropagating in a curved coordinate space corresponding to the selectedcoordinate transformation. Constitutive parameters of the transformationmedium can be obtained from the equations:{tilde over (∈)}^(i′j′) =|det(Λ)|⁻¹Λ_(i) ^(i′)Λ_(j) ^(j′)∈^(ij)  (1){tilde over (μ)}^(i′j′) =|det(Λ)|⁻¹Λ_(i) ^(i′)Λ_(j) ^(j′)μ^(ij)  (2)where {tilde over (∈)} and {tilde over (μ)} are the permittivity andpermeability tensors of the transformation medium, ∈ and μ are thepermittivity and permeability tensors of the original medium in theuntransformed coordinate space, and

$\begin{matrix}{\Lambda_{i}^{i^{\prime}} = \frac{\partial x^{i^{\prime}}}{\partial x^{i}}} & (3)\end{matrix}$is the Jacobian matrix corresponding to the coordinate transformation.In some applications, the coordinate transformation is a one-to-onemapping of locations in the untransformed coordinate space to locationsin the transformed coordinate space, and in other applications thecoordinate transformation is a one-to-many mapping of locations in theuntransformed coordinate space to locations in the transformedcoordinate space. Some coordinate transformations, such as one-to-manymappings, may correspond to a transformation medium having a negativeindex of refraction. In some applications, only selected matrix elementsof the permittivity and permeability tensors need satisfy equations (1)and (2), e.g. where the transformation optics response is for a selectedpolarization only. In other applications, a first set of permittivityand permeability matrix elements satisfy equations (1) and (2) with afirst Jacobian Λ, corresponding to a first transformation opticsresponse for a first polarization of electromagnetic waves, and a secondset of permittivity and permeability matrix elements, orthogonal (orotherwise complementary) to the first set of matrix elements, satisfyequations (1) and (2) with a second Jacobian Λ′, corresponding to asecond transformation optics response for a second polarization ofelectromagnetic waves. In yet other applications, reduced parameters areused that may not satisfy equations (1) and (2), but preserve productsof selected elements in (1) and selected elements in (2), thuspreserving dispersion relations inside the transformation medium (see,for example, D. Schurig et al (2), supra, and W. Cai et al, “Opticalcloaking with metamaterials,” Nature Photonics 1, 224 (2007), hereinincorporated by reference). Reduced parameters can be used, for example,to substitute a magnetic response for an electric response, or viceversa. While reduced parameters preserve dispersion relations inside thetransformation medium (so that the ray or wave trajectories inside thetransformation medium are unchanged from those of equations (1) and(2)), they may not preserve impedance characteristics of thetransformation medium, so that rays or waves incident upon a boundary orinterface of the transformation medium may sustain reflections (whereasin general a transformation medium according to equations (1) and (2) issubstantially nonreflective). The reflective or scatteringcharacteristics of a transformation medium with reduced parameters canbe substantially reduced or eliminated by a suitable choice ofcoordinate transformation, e.g. by selecting a coordinate transformationfor which the corresponding Jacobian Λ (or a subset of elements thereof)is continuous or substantially continuous at a boundary or interface ofthe transformation medium (see, for example, W. Cai et al, “Nonmagneticcloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007),herein incorporated by reference).

In general, constitutive parameters (such as permittivity andpermeability) of a medium responsive to an electromagnetic wave can varywith respect to a frequency of the electromagnetic wave (orequivalently, with respect to a wavelength of the electromagnetic wavein vacuum or in a reference medium). Thus, a medium can haveconstitutive parameters ∈₁, μ₁, etc. at a first frequency, andconstitutive parameters ∈₂, μ₂, etc. at a second frequency; and so onfor a plurality of constitutive parameters at a plurality offrequencies. In the context of a transformation medium, constitutiveparameters at a first frequency can provide a first response toelectromagnetic waves at the first frequency, corresponding to a firstselected coordinate transformation, and constitutive parameters at asecond frequency can provide a second response to electromagnetic wavesat the second frequency, corresponding to a second selected coordinatetransformation; and so on: a plurality of constitutive parameters at aplurality of frequencies can provide a plurality of responses toelectromagnetic waves corresponding to a plurality of coordinatetransformations. In some embodiments the first response at the firstfrequency is substantially nonzero (i.e. one or both of ∈₁ and μ₁ issubstantially non-unity), corresponding to a nontrivial coordinatetransformation, and a second response at a second frequency issubstantially zero (i.e. ∈₂ and μ₂ are substantially unity),corresponding to a trivial coordinate transformation (i.e. a coordinatetransformation that leaves the coordinates unchanged); thus,electromagnetic waves at the first frequency are refracted(substantially according to the nontrivial coordinate transformation),and electromagnetic waves at the second frequency are substantiallynonrefracted. Constitutive parameters of a medium can also change withtime (e.g. in response to an external input or control signal), so thatthe response to an electromagnetic wave can vary with respect tofrequency and/or time. Some embodiments may exploit this variation withfrequency and/or time to provide respective frequency and/or timemultiplexing/demultiplexing of electromagnetic waves. Thus, for example,a transformation medium can have a first response at a frequency at timet₁, corresponding to a first selected coordinate transformation, and asecond response at the same frequency at time t₂, corresponding to asecond selected coordinate transformation. As another example, atransformation medium can have a response at a first frequency at timet₁, corresponding to a selected coordinate transformation, andsubstantially the same response at a second frequency at time t₂. In yetanother example, a transformation medium can have, at time t₁, a firstresponse at a first frequency and a second response at a secondfrequency, whereas at time t₂, the responses are switched, i.e., thesecond response (or a substantial equivalent thereof) is at the firstfrequency and the first response (or a substantial equivalent thereof)is at the second frequency. The second response can be a zero orsubstantially zero response. Other embodiments that utilize frequencyand/or time dependence of the transformation medium will be apparent toone of skill in the art.

Constitutive parameters such as those of equations (1) and (2) (orreduced parameters derived therefrom) can be realized usingartificially-structured materials. Generally speaking, theelectromagnetic properties of artificially-structured materials derivefrom their structural configurations, rather than or in addition totheir material composition.

In some embodiments, the artificially-structured materials are photoniccrystals. Some exemplary photonic crystals are described in J. D.Joannopoulos et al, Photonic Crystals Molding the Flow of Light, 2^(nd)Edition, Princeton Univ. Press, 2008, herein incorporated by reference.In photonic crystals, photonic dispersion relations and/or photonic bandgaps are engineered by imposing a spatially-varying pattern on anelectromagnetic material (e.g. a conducting, magnetic, or dielectricmaterial) or a combination of electromagnetic materials. The photonicdispersion relations translate to effective constitutive parameters(e.g. permittivity, permeability, index of refraction) for the photoniccrystal. The spatially-varying pattern is typically periodic,quasi-periodic, or colloidal periodic, with a length scale comparable toan operating wavelength of the photonic crystal.

In other embodiments, the artificially-structured materials aremetamaterials. Some exemplary metamaterials are described in R. A. Hydeet al, “Variable metamaterial apparatus,” U.S. patent application Ser.No. 11/355,493; D. Smith et al, “Metamaterials,” InternationalApplication No. PCT/US2005/026052; D. Smith et al, “Metamaterials andnegative refractive index,” Science 305, 788 (2004); D. Smith et al,“Indefinite materials,” U.S. patent application Ser. No. 10/525,191; C.Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission LineTheory and Microwave Applications, Wiley-Interscience, 2006; N. Enghetaand R. W. Ziolkowski, eds., Metamaterials: Physics and EngineeringExplorations, Wiley-Interscience, 2006; and A. K. Sarychev and V. M.Shalaev, Electrodynamics of Metamaterials, World Scientific, 2007; eachof which is herein incorporated by reference.

Metamaterials generally feature subwavelength elements, i.e. structuralelements with portions having electromagnetic length scales smaller thanan operating wavelength of the metamaterial, and the subwavelengthelements have a collective response to electromagnetic radiation thatcorresponds to an effective continuous medium response, characterized byan effective permittivity, an effective permeability, an effectivemagnetoelectric coefficient, or any combination thereof. For example,the electromagnetic radiation may induce charges and/or currents in thesubwavelength elements, whereby the subwavelength elements acquirenonzero electric and/or magnetic dipole moments. Where the electriccomponent of the electromagnetic radiation induces electric dipolemoments, the metamaterial has an effective permittivity; where themagnetic component of the electromagnetic radiation induces magneticdipole moments, the metamaterial has an effective permeability; andwhere the electric (magnetic) component induces magnetic (electric)dipole moments (as in a chiral metamaterial), the metamaterial has aneffective magnetoelectric coefficient. Some metamaterials provide anartificial magnetic response; for example, split-ring resonators(SRRs)—or other LC or plasmonic resonators—built from nonmagneticconductors can exhibit an effective magnetic permeability (c.f. J. B.Pendry et al, “Magnetism from conductors and enhanced nonlinearphenomena,” IEEE Trans. Micro. Theo. Tech. 47, 2075 (1999), hereinincorporated by reference). Some metamaterials have “hybrid”electromagnetic properties that emerge partially from structuralcharacteristics of the metamaterial, and partially from intrinsicproperties of the constituent materials. For example, G. Dewar, “A thinwire array and magnetic host structure with n<0,” J. Appl. Phys. 97,10Q101 (2005), herein incorporated by reference, describes ametamaterial consisting of a wire array (exhibiting a negativepermeability as a consequence of its structure) embedded in anonconducting ferrimagnetic host medium (exhibiting an intrinsicnegative permeability). Metamaterials can be designed and fabricated toexhibit selected permittivities, permeabilities, and/or magnetoelectriccoefficients that depend upon material properties of the constituentmaterials as well as shapes, chiralities, configurations, positions,orientations, and couplings between the subwavelength elements. Theselected permittivites, permeabilities, and/or magnetoelectriccoefficients can be positive or negative, complex (having loss or gain),anisotropic, variable in space (as in a gradient index lens), variablein time (e.g. in response to an external or feedback signal), variablein frequency (e.g. in the vicinity of a resonant frequency of themetamaterial), or any combination thereof. The selected electromagneticproperties can be provided at wavelengths that range from radiowavelengths to infrared/visible wavelengths; the latter wavelengths areattainable, e.g., with nanostructured materials such as nanorod pairs ornano-fishnet structures (c.f. S. Linden et al, “Photonic metamaterials:Magnetism at optical frequencies,” IEEE J. Select. Top. Quant. Elect.12, 1097 (2006) and V. Shalaev, “Optical negative-index metamaterials,”Nature Photonics 1, 41 (2007), both herein incorporated by reference).An example of a three-dimensional metamaterial at optical frequencies,an elongated-split-ring “woodpile” structure, is described in M. S. Rillet al, “Photonic metamaterials by direct laser writing and silverchemical vapour deposition,” Nature Materials advance onlinepublication, May 11, 2008, (doi:10.1038/nmat2197).

While many exemplary metamaterials are described as including discreteelements, some implementations of metamaterials may include non-discreteelements or structures. For example, a metamaterial may include elementscomprised of sub-elements, where the sub-elements are discretestructures (such as split-ring resonators, etc.), or the metamaterialmay include elements that are inclusions, exclusions, layers, or othervariations along some continuous structure (e.g. etchings on asubstrate). Some examples of layered metamaterials include: a structureconsisting of alternating doped/intrinsic semiconductor layers (cf. A.J. Hoffman, “Negative refraction in semiconductor metamaterials,” NatureMaterials 6, 946 (2007), herein incorporated by reference), and astructure consisting of alternating metal/dielectric layers (cf. A.Salandrino and N. Engheta, “Far-field subdiffraction optical microscopyusing metamaterial crystals: Theory and simulations,” Phys. Rev. B 74,075103 (2006); and Z. Jacob et al, “Optical hyperlens: Far-field imagingbeyond the diffraction limit,” Opt. Exp. 14, 8247 (2006); each of whichis herein incorporated by reference). The metamaterial may includeextended structures having distributed electromagnetic responses (suchas distributed inductive responses, distributed capacitive responses,and distributed inductive-capacitive responses). Examples includestructures consisting of loaded and/or interconnected transmission lines(such as microstrips and striplines), artificial ground plane structures(such as artificial perfect magnetic conductor (PMC) surfaces andelectromagnetic band gap (EGB) surfaces), and interconnected/extendednanostructures (nano-fishnets, elongated SRR woodpiles, etc.).

With reference now to FIG. 1, an illustrative embodiment is depictedthat includes a negatively-refractive focusing structure 110. This andother drawings, unless context dictates otherwise, can represent aplanar view of a three-dimensional embodiment, or a two-dimensionalembodiment (e.g. in FIG. 1 where the structures are positioned inside ametallic or dielectric slab waveguide oriented normal to the page). Thenegatively-refractive focusing structure receives and negativelyrefracts electromagnetic energy, depicted as solid rays 102 (the use ofa ray description, in FIG. 1 and elsewhere, is a heuristic conveniencefor purposes of visual illustration, and is not intended to connote anylimitations or assumptions of geometrical optics; further, the elementsdepicted in FIG. 1 can have spatial dimensions that are variously lessthan, greater than, or comparable to a wavelength of interest). Thenegatively-refracted electromagnetic energy converges towards aninterior focusing region 120 positioned inside the negatively-refractivefocusing structure 110; in this example, the interior focusing region120 is depicted as a slab having a thickness equal an axial extent 122of the interior focusing region. The axial extent 122 corresponds to anaxial direction indicated by the axial unit vector 160, with transverseunit vectors 161 and 162 defined perpendicular thereto. In FIG. 1, theelectromagnetic energy radiates from exemplary electromagnetic sources101 in an exterior field region 130, the exterior field region beingpositioned outside the negatively-refractive focusing structure. In thisexample, the exterior field region 130 is depicted as a slab having athickness equal to an axial extent 132 of the exterior field region. Theelectromagnetic sources 101 in the exterior field region correspond toelectromagnetic images 103 in the interior focusing region. The axialextent 132 of the exterior field region (spanned, in this example, bythe electromagnetic sources 101) exceeds the axial extent 122 of theinterior focusing region (spanned, in this example, by theelectromagnetic images 103), thus demonstrating that thenegatively-refractive focusing structure provides an axial magnificationless than one, and in this example the axial magnification correspondsto a ratio of the axial extent of the interior focusing region to theaxial extent of the exterior field region. Embodiments optionallyinclude one or more electromagnetic sensors (schematically depicted asellipses 150) positioned within the interior focusing region (in thepresented illustrative representation, sensors are linearly positionedalong the axial extent 122 of the interior focusing region, but this isnot intended to be limiting).

In general, embodiments provide a negatively-refractive focusingstructure having an interior focusing region and an exterior fieldregion; electromagnetic energy that radiates from the exterior fieldregion, and couples to the negatively-refractive focusing structure, issubsequently substantially concentrated in the interior focusing region.For example, in some applications each object point in the exteriorfield region defines a point spread function and a correspondingenclosed energy region (e.g. a region wherein some selected 13 such as50%, 75%, or 90%—of electromagnetic energy that radiates from the objectpoint is concentrated), and the interior focusing region is a union ofthe enclosed energy regions for the object points that compose theexterior field region. The negatively-refractive focusing structureprovides an axial magnification, and in some applications the axialmagnification corresponds to a ratio where the divisor is an axialseparation between first and second object points and the dividend is anaxial separation between centroids of first and second point spreadfunctions corresponding to the first and second object points. In someembodiments, the interior focusing region may be a planar orsubstantially planar slab (e.g. 120 in FIG. 1) having a slab thicknessproviding the axial extent of the interior focusing region (e.g. 122 inFIG. 1). In other embodiments, the interior focusing region may be anon-planar slab-like region, e.g. a cylindrically-, spherically-,ellipsoidally-, or otherwise-curved slab having a slab thicknessproviding the axial extent of the interior focusing region. In otherembodiments, the interior focusing region may be neither planar norslab-like. In some embodiments the negatively-refractive focusingstructure defines an optical axis as a symmetry or central axis of thenegatively-refractive focusing structure, and the optical axis providesan axial direction, with transverse directions defined perpendicularthereto. More generally, one may define an axial direction correspondingto an axial extent of the interior focusing region, with transversedirections defined perpendicular thereto. This is consistent with FIG.1, where the interior focusing region is a planar slab, and the axialdirection corresponds to a unit vector normal to the slab. Where theinterior focusing region is curved, the axial direction can vary alongthe transverse extent of the focusing region. For example, where theinterior focusing region is a cylindrically- or spherically-curved slab,the axial direction corresponds to a radius unit vector (and thetransverse directions correspond to height/azimuth unit vectors orazimuth/zenith unit vectors, respectively); where the interior focusingregion is an otherwise-curved slab, the axial direction corresponds to avector locally normal to the slab surface (and the transverse directionscorrespond to orthogonal unit vectors locally tangent to the slabsurface).

In some embodiments a negatively-refractive focusing structure, such asthat depicted in FIG. 1, includes a transformation medium. For example,the ray trajectories 102 in FIG. 1 correspond to a coordinatetransformation that is multiple-valued and includes both a coordinateinversion and a uniform spatial contraction along the axial direction160 (within the axial extent of the negatively-refractive focusingstructure 110); this coordinate transformation can be used to identifyconstitutive parameters for a corresponding transformation medium (e.g.as provided in equations (1) and (2), or reduced parameters obtainedtherefrom) that responds to electromagnetic radiation as in FIG. 1.Explicitly, for the example of FIG. 1, defining z as an untransformedaxial coordinate and z′ as a transformed axial coordinate (where theaxial coordinates are measured along the axial direction 160), themultiple-valued coordinate transformation is depicted in FIG. 2, withfirst, second, and third branches 201, 202, and 203 corresponding tofunctions z′=f₁(z), z′=f₂(z), and z′=f₃(z), respectively. The firstbranch 201 is an identity transformation (f₁(z)=z) and maps anuntransformed coordinate region 220 to the exterior field region 130.The second branch 202 includes an axial coordinate inversion and auniform axial coordinate contraction, and maps the untransformedcoordinate region 220 to the interior focusing region 120. The thirdbranch 203 is a shifted itenity transformation (f₃(z)=z+C, where C is aconstant). The figure also indicates the axial extent of thenegatively-refractive focusing structure 110 on the z′-axis (coinciding,in this example, with the range of the second branch 202). On the secondbranch, defining a scale factor

$\begin{matrix}{{s = {\frac{\mathbb{d}z^{\prime}}{\mathbb{d}z} = {f_{2}^{\prime}(z)}}},} & (4)\end{matrix}$the example of FIGS. 1-2 presents a constant negative scale factor−1<s<0 within the negatively-refractive focusing structure 110,corresponding to a coordinate inversion (whereby s<0) and a uniformspatial contraction (whereby |s|<1; in some instances within thisdocument, as shall be apparent to one of skill in the art, the use ofthe term “scale factor,” when used in the context of a spatialcontraction, may refer to the absolute value of a negative scale factorsuch as described here). Supposing that the negatively-refractivefocusing structure is surrounded by an ambient isotropic medium withconstitutive parameters ∈^(ij)∈δ^(ij), μ^(ij)=μδ^(ij) (where δ^(ij)denotes the Kronecker delta-function, with δ^(ij)=1 for i=j and δ^(ij)=0for i≠j), the constitutive parameters of the transformation medium areobtained from equations (1) and (2) and are given by (in a basis withunit vectors 161, 162, and 160, respectively, in FIG. 1)

$\begin{matrix}{{\overset{\sim}{ɛ} = {\begin{pmatrix}s^{- 1} & 0 & 0 \\0 & s^{- 1} & 0 \\0 & 0 & s\end{pmatrix}ɛ}},\mspace{14mu}{\overset{\sim}{\mu} = {\begin{pmatrix}s^{- 1} & 0 & 0 \\0 & s^{- 1} & 0 \\0 & 0 & s\end{pmatrix}{\mu.}}}} & (5)\end{matrix}$Thus, the uniform spatial dilation of FIGS. 1-2 corresponds to atransformation medium that is a uniform uniaxial medium. Moreover, thescale factor is negative, so that the constitutive parameters inequation (5) are negative, and the transformation medium is anegatively-refractive medium defining a negative index of refraction.

In some embodiments, the negatively-refractive focusing structureincludes a transformation medium that provides a non-uniform spatialdilation. An example is depicted in FIG. 3 and the correspondingmultiple-valued coordinate transformation is depicted in FIG. 4. In FIG.3, as in FIG. 1, a negatively-refractive focusing structure 110 providesan interior focusing region 120 for electromagnetic energy that radiatesfrom an exterior field region 130. In contrast to FIG. 1, however, theembodiment of FIG. 3 provides a non-uniform scale factor s (the slope ofthe mapping function z′=f₂ (z) for the second branch 202 of themultiple-valued coordinate transformation); indeed, the scale factor inthis relation satisfies, in some interval(s), the relation −1<s<0(corresponding to a local spatial contraction and coordinate inversion),and in other interval(s), the relation s<−1 (corresponding to a localspatial dilation and coordinate inversion). The constitutive relationsare again given by equations (5), where s is variable in the axialdirection, and the transformation medium is a non-uniform uniaxialmedium (again with negative constitutive parameters and defining anegative index of refraction).

More generally, embodiments of a negatively-refractive focusingstructure, operable to provide an interior focusing region forelectromagnetic energy that radiates from an exterior field region, maycomprise a transformation medium, the transformation mediumcorresponding to a multiple-valued coordinate transformation that mapsan untransformed region to the exterior field region, and further mapsthe untransformed region to the interior focusing region; and theconstitutive relations of this transformation medium may be implementedwith an artificially-structured material (such as a metamaterial), asdescribed previously. In some embodiments, the coordinate transformationincludes a coordinate inversion and spatial contraction along an axialdirection of the interior focusing region, and a scale factor of thespatial contraction (within the interior focusing region) may correspondto a ratio of an axial extent of the interior focusing region to anaxial extent of the exterior field region. This is consistent with FIGS.2 and 4, where the slope triangle 200, indicating a scale factor in theinterior focusing region, is similar or substantially similar to atriangle with a base 220 (equal to 130, for a first branch 201 that isan identity transformation) and a height 120. Just as the axialdirection can vary along a transverse extent of the interior focusingregion, the direction of the coordinate inversion/contraction can varyas well. Thus, for example, a substantially cylindrically- orspherically-curved interior focusing region may correspond to a (uniformor non-uniform) inversion/contraction of a cylindrical or sphericalradius coordinate; a substantially ellipsoidally-curved interiorfocusing region may correspond to a (uniform or non-uniform)inversion/contraction of a confocal ellipsoidal coordinate; etc.

The negatively-refractive focusing structure 110 is depicted in FIGS. 1and 3 as a planar slab, but this is a schematic illustration and is notintended to be limiting. In various embodiments thenegatively-refractive focusing structure can be a cylindrically-,spherically-, or ellipsoidally-curved slab, or any other slab- ornon-slab-like structure configured to provide an interior focusingregion for negatively-refracted electromagnetic energy with an axialmagnification substantially less than one. Some embodiments, such asthat depicted in FIG. 5, define an input surface region 510 as a surfaceregion of the negatively-refractive focusing structure 110 that receiveselectromagnetic radiation from an adjacent region 500, and this inputsurface region may be substantially nonreflective of the receivedelectromagnetic radiation. For example, where the negatively-refractivefocusing structure is a transformation medium, equations (1) and (2)generally provide a medium that is substantially nonreflective. Moregenerally, the input surface region may be substantially nonreflectiveby virtue of a substantial impedance-matching to the adjacent region.With impedance-matching, a wave impedance of the input surface region issubstantially equal to a wave impedance of the adjacent region. The waveimpedance of an isotropic medium is

$\begin{matrix}{Z_{0} = \sqrt{\frac{\mu}{ɛ}}} & (6)\end{matrix}$while the wave impedance of a generally anisotropic medium is a tensorquantity, e.g. as defined in L. M. Barkovskii and G. N. Borzdov, “Theimpedance tensor for electromagnetic waves in anisotropic media,” J.Appl. Spect. 20, 836 (1974) (herein incorporated by reference). In someembodiments an impedance-matching is a substantial matching of everymatrix element of the wave impedance tensor (i.e. to provide asubstantially nonreflective interface for all incident polarizations);in other embodiments an impedance-matching is a substantial matching ofonly selected matrix elements of the wave impedance tensor (e.g. toprovide a substantially nonreflective interface for a selectedpolarization only). In some embodiments, the adjacent region defines apermittivity ∈₁ and a permeability μ₁, where either or both parametersmay be substantially unity or substantially non-unity; the input surfaceregion defines a permittivity ∈₂ and a permeability μ₂, where either orboth parameters may be substantially unity or substantially non-unity;and the impedance-matching condition implies

$\begin{matrix}{\frac{ɛ_{2}}{ɛ_{1}} \cong \frac{\mu_{2}}{\mu_{1}}} & (7)\end{matrix}$where ∈₂ and μ₂ may be tensor quantities. Defining a surface normaldirection and a surface parallel direction (e.g. depicted as elements521 and 522, respectively, in FIG. 5), some embodiments provide a inputsurface region that defines: a surface normal permittivity ∈₂ ^(⊥)corresponding to the surface normal direction and a surface parallelpermittivity ∈₂ ^(∥) corresponding to the surface parallel direction;and/or a surface normal permeability ∈₂ ^(⊥) corresponding to thesurface normal direction and a surface parallel permeability ∈₂ ^(∥)corresponding to the surface parallel direction; and theimpedance-matching condition may imply (in addition to equation (7)) oneor both of the following conditions:

$\begin{matrix}{{\frac{ɛ_{2}^{\bot}}{ɛ_{1}} \cong \frac{ɛ_{1}}{ɛ_{2}^{}}},\mspace{14mu}{\frac{\mu_{2}^{\bot}}{\mu_{1}} \cong {\frac{\mu_{1}}{\mu_{2}^{}}.}}} & (8)\end{matrix}$Where the input surface region is a curved surface region (e.g. as inFIG. 5), the surface normal direction and the surface parallel directioncan vary with position along the input surface region.

Some embodiments provide one or more electromagnetic sensors positionedwithin the interior focusing region of the negatively-refractivefocusing structure. In general, electromagnetic sensors, such as thosedepicted FIG. 1 and in other embodiments, are electromagnetic deviceshaving a detectable response to received or absorbed electromagneticenergy. Electromagnetic sensors can include antennas (such as wire/loopantennas, horn antennas, reflector antennas, patch antennas, phasedarray antennas, etc.), solid-state photodetectors (such as photodiodes,CCDs, and photoresistors), vacuum photodetectors (such as phototubes andphotomultipliers) chemical photodetectors (such as photographicemulsions), cryogenic photodetectors (such as bolometers),photoluminescent detectors (such as phosphor powders or fluorescentdyes/markers), MEMS detectors (such as microcantilever arrays withelectromagnetically responsive materials or elements) or any otherdevices operable to detect and/or transduce electromagnetic energy. Insome embodiments the electromagnetic sensors include devices ormaterials that may undergo a change in state (such as a phase change orchemical reaction) in response to absorbed or received electromagneticenergy, e.g. a photoresist, a light-sensitive polymer, etc. In otherembodiments the electromagnetic sensors include devices or materialshaving a nonlinear response to absorbed or received electromagneticradiation, e.g. a nonlinear optical material. Some embodiments include aplurality of electromagnetic sensors positioned within the interiorfocusing region. A first example is a multiplet of sensors operable at acorresponding multiplet of wavelengths or wavelength bands, i.e. a firstsensor operable at a first wavelength/wavelength band, a second sensoroperable at a second wavelength/wavelength band, etc. A second exampleis a focal plane array of sensors or sensor multiplets (e.g. a Bayer orFoveon sensor). A third example is a phased array of antennas. Theplurality of sensors can be axially distributed (as in FIG. 1); forexample, the axial extent of the interior focusing region may admit aplurality of parallel focal plane sensor arrays.

In some embodiments the negatively-refractive focusing structureprovides an interior focusing region with an axial magnificationsubstantially less than one for electromagnetic energy at a selectedfrequency/frequency band and/or a selected polarization. The selectedfrequency or frequency band may be selected from a range that includesradio frequencies, microwave frequencies, millimeter- orsubmillimeter-wave frequencies, THz-wave frequencies, opticalfrequencies (e.g. variously corresponding to soft x-rays, extremeultraviolet, ultraviolet, visible, near-infrared, infrared, or farinfrared light), etc. The selected polarization may be a particular TEpolarization (e.g. where the electric field is in a particular directiontransverse to the axial direction, as with s-polarized electromagneticenergy), a particular TM polarization (e.g. where the magnetic field isin a particular direction transverse to the axial direction, as withp-polarized electromagnetic energy), a circular polarization, etc.(other embodiments provide an interior focusing region with an axialmagnification substantially less than one that is substantially the sameinterior focusing region with substantially the same axial magnificationfor any polarization of electromagnetic energy, e.g. for unpolarizedelectromagnetic energy).

In other embodiments the negatively-refractive focusing structureprovides a first interior focusing region with a first axialmagnification substantially less than one for electromagnetic energy ata first frequency, and a second interior focusing region with a secondaxial magnification substantially less than one for electromagneticenergy at a second frequency. The first axial magnification may bedifferent than or substantially equal to the first axial magnification,and the first and second interior focusing regions may be substantially(or completely) non-overlapping, partially overlapping or substantially(or completely) overlapping. For embodiments that recite first andsecond frequencies, the first and second frequencies may be selectedfrom the frequency categories in the preceding paragraph. Moreover, forthese embodiments, the recitation of first and second frequencies maygenerally be replaced by a recitation of first and second frequencybands, again selected from the above frequency categories. Theseembodiments providing a negatively-refractive focusing structureoperable at first and second frequencies may include a transformationmedium having an adjustable response to electromagnetic radiation. Forexample, the transformation medium may have a response toelectromagnetic radiation that is adjustable (e.g. in response to anexternal input or control signal) between a first response and a secondresponse, the first response providing the first interior focusingregion for electromagnetic energy at the first frequency, and the secondresponse providing the second interior focusing region forelectromagnetic energy at the second frequency. A transformation mediumwith an adjustable electromagnetic response may be implemented withvariable metamaterials, e.g. as described in R. A. Hyde et al, supra.Other embodiments of a negatively-refractive focusing structure operableat first and second frequencies may include transformation medium havinga frequency-dependent response to electromagnetic radiation,corresponding to frequency-dependent constitutive parameters. Forexample, the frequency-dependent response at a first frequency mayprovide a first interior focusing region for electromagnetic energy atthe first frequency, and the frequency-dependent response at a secondfrequency may provide second interior focusing region forelectromagnetic energy at the second frequency. A transformation mediumhaving a frequency-dependent response to electromagnetic radiation canbe implemented with artificially-structured materials such asmetamaterials; for example, a first set of metamaterial elements havinga response at the first frequency may be interleaved with a second setof metamaterial elements having a response at the second frequency.

An illustrative embodiment is depicted as a process flow diagram in FIG.6. Flow 600 includes operation 610—negatively refracting anelectromagnetic wave at a surface region, the surface region defining asurface normal direction. For example, a negatively-refractive focusingstructure, such as that depicted as element 110 in FIG. 5, may includean input surface region 510 that negatively refracts electromagneticenergy incident upon the input surface region from an adjacent region,and the negatively-refractive focusing structure may include atransformation medium that provides a coordinate inversion (for acoordinate corresponding to a direction normal to the surface, e.g. thedirection 521 in FIG. 5), the coordinate inversion corresponding to anegatively-refractive response of the transformation medium. Flow 600further includes operation 620—spatially contracting the refractedelectromagnetic wave along a contraction direction, the contractiondirection corresponding to the surface normal direction. For example, anegatively-refractive focusing structure, such as that depicted aselement 110 in FIGS. 1 and 3, may spatially contract refractedelectromagnetic energy 102 along an axial direction (e.g. the direction160 in FIGS. 1 and 3) to provide an axial extent of an interior focusingregion 120 less than an axial extent of an exterior field region 130(the ratio of axial extents corresponding to a provided axialmagnification), and the negatively-refractive focusing structure mayinclude a transformation medium that provides a coordinate contraction(for an axial coordinate corresponding to the axial direction 160), thecoordinate contraction having a scale factor corresponding to theprovided axial magnification. Operation 620 optionally includessub-operation 622—spatially contracting a first component of therefracted electromagnetic wave at a first frequency along thecontraction direction—and sub-operation 624—spatially contracting asecond component of the refracted electromagnetic wave at a secondfrequency along the contraction direction. For example, anegatively-refractive focusing structure may provide a first interiorfocusing region with a first axial magnification for electromagneticenergy at a first frequency and a second interior focusing region with asecond axial magnification for electromagnetic energy at a secondfrequency, where the second axial magnification may be different than orsubstantially equal to the first axial magnification; and thisnegatively-refractive focusing structure operable at first and secondfrequencies may include a transformation medium having an adjustableresponse to electromagnetic radiation, or a transformation medium havinga frequency-dependent response to electromagnetic radiation. Flow 600optionally includes operation 630—sensing the electromagnetic wave atone or more locations within a focusing region that is provided by thenegatively refracting and the spatially contracting. For example, anegatively-refractive focusing structure 110, such as that depicted inFIGS. 1 and 3, may provide an interior focusing region 120, and one ormore electromagnetic sensors, such as those depicted as elements 150 inFIG. 1, may be positioned within the interior focusing region todetect/receive/absorb the electromagnetic energy 102.

Another illustrative embodiment is depicted as a process flow diagram inFIG. 7. Flow 700 includes operation 710—determining electromagneticparameters that define a negative refractive index in a spatial region,the electromagnetic parameters providing an axial magnificationsubstantially less than one for an interior focusing region within thespatial region. For example, the spatial region may be a volume thatencloses a negatively-refractive focusing structure, such as thatdepicted as element 110 in FIGS. 1 and 3, and the determinedelectromagnetic parameters may be the electromagnetic parameters of thenegatively-refractive focusing structure. The negatively-refractivefocusing structure may include a transformation medium, where thedetermined electromagnetic parameters satisfy or substantially satisfyequations (1) and (2), as described above; or, the determinedelectromagnetic parameters may be reduced parameters (as discussedearlier) where the corresponding non-reduced parameters satisfyequations (1) and (2). In some embodiments, the determining of theelectromagnetic parameters includes: determining a coordinatetransformation (such as those depicted in FIGS. 2 and 4); thendetermining electromagnetic parameters for a correspondingtransformation medium (e.g. with equations (1) and (2)); then,optionally, reducing the electromagnetic parameters (e.g. to at leastpartially substitute a magnetic response for an electromagneticresponse, or vice versa, as discussed above). Operation 710 optionallyincludes sub-operation 712—for electromagnetic waves at a firstfrequency, determining a first subset of the electromagnetic parametersproviding a first axial magnification substantially less than one for afirst interior focusing subregion within the interior focusingregion—and sub-operation 714—for electromagnetic waves at a secondfrequency, determining a second subset of the electromagnetic parametersproviding a second axial magnification substantially less than one for asecond interior focusing subregion within the interior focusing region.For example, the determined electromagnetic parameters may be theelectromagnetic parameters of a negatively-refractive focusing structureproviding a first interior focusing region with a first axialmagnification for electromagnetic energy at a first frequency and asecond interior focusing region with a second axial magnification forelectromagnetic energy at a second frequency. The negatively-refractivefocusing structure may include a transformation medium having anadjustable response to electromagnetic radiation, e.g. adjustablebetween a first response, corresponding to the first subset of theelectromagnetic parameters, and a second response, corresponding to thesecond subset of the electromagnetic parameters. Or, thenegatively-refractive focusing structure may include a transformationmedium having a frequency-dependent response to electromagneticradiation, corresponding to frequency-dependent constitutive parameters,so that the first and second subsets of the electromagnetic parametersare values of the frequency-dependent constitutive parameters at thefirst and second frequencies, respectively. Flow 700 optionally furtherincludes operation 720—selecting one or more positions of one or moreelectromagnetic sensors within the spatial region. For example,electromagnetic sensors may be positioned in a phased array, an focalplane array, an axially-distributed arrangement, etc. Flow 700optionally further includes operation 730—configuring anartificially-structured material having an effective electromagneticresponse that corresponds to the electromagnetic parameters in thespatial region. For example, the configuring may include configuring thestructure(s) and/or the materials that compose a photonic crystal or ametamaterial. Operation 730 optionally includes determining anarrangement of a plurality of electromagnetically responsive elementshaving a plurality of individual responses, the plurality of individualresponses composing the effective electromagnetic response. For example,the determining may include determining the positions, orientations, andindividual response parameters (spatial dimensions, resonantfrequencies, linewidths, etc.) of a plurality of metamaterial elementssuch as split-ring resonators, wire or nanowire pairs, etc. Operation730 optionally includes configuring at least oneelectromagnetically-responsive structure to arrange a plurality ofdistributed electromagnetic responses, the plurality of distributedelectromagnetic responses composing the effective electromagneticresponse. For example, the configuring may include configuring thedistribution of loads and interconnections on a transmission linenetwork, configuring an arrangement of layers in a layered metamaterial,configuring a pattern of etching or deposition (as with a nano-fishnetstructure), etc.

With reference now to FIG. 8, an illustrative embodiment is depicted asa system block diagram. The system 800 includes a focusing unit 810optionally coupled to a controller unit 830. The focusing unit 810 mayinclude a negatively-refractive focusing structure such as that depictedas element 110 in FIGS. 1 and 3. The negatively-refractive focusingstructure may be a variable negatively-refractive focusing structure,such as a variable metamaterial responsive to one or more control inputsto vary one or more focusing characteristics (axial magnification,operating frequency/frequency band, operating polarization, effectivecoordinate transformation for a transformation medium, etc.); and thecontroller unit 830 may include control circuitry that provides one ormore control inputs to the variable negatively-refractive focusingstructure. The system 800 optionally further includes a sensing unit 820that may include one or more sensors, such as those depicted as elements150 in FIG. 1, and associated circuitry such as receiver circuitry,detector circuitry, and/or signal processing circuitry. The sensing unit820 is optionally coupled to the controller unit 830, and in someembodiments the controller unit 830 includes circuitry for coordinatingor synchronizing the operation of the focusing unit 810 and the sensingunit 820. The controller unit 830 may include circuitry responsive tosensor data (from the sensor unit 820) to vary the focusingcharacteristics of the focusing structure. As a first example, thecontroller unit may include circuitry responsive to the sensor data toidentify a frequency/polarization of received energy, and adjust thefocusing unit to an operating frequency/polarization substantially equalto the frequency/polarization of the received energy. As a secondexample, the controller unit may include circuitry responsive to thesensor data to identify a target interior focusing region (and/or atarget axial magnification), and corresponding adjust the focusingsystem whereby a negatively-refractive focusing structure provides aninterior focusing region substantially equal to the target interiorfocusing region (and/or an axial magnification substantially equal tothe target axial magnification).

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and/or examples. Insofar as such block diagrams, flowcharts, and/orexamples contain one or more functions and/or operations, it will beunderstood by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof. In one embodiment,several portions of the subject matter described herein may beimplemented via Application Specific Integrated Circuits (ASICs), FieldProgrammable Gate Arrays (FPGAs), digital signal processors (DSPs), orother integrated formats. However, those skilled in the art willrecognize that some aspects of the embodiments disclosed herein, inwhole or in part, can be equivalently implemented in integratedcircuits, as one or more computer programs running on one or morecomputers (e.g., as one or more programs running on one or more computersystems), as one or more programs running on one or more processors(e.g., as one or more programs running on one or more microprocessors),as firmware, or as virtually any combination thereof, and that designingthe circuitry and/or writing the code for the software and or firmwarewould be well within the skill of one of skill in the art in light ofthis disclosure. In addition, those skilled in the art will appreciatethat the mechanisms of the subject matter described herein are capableof being distributed as a program product in a variety of forms, andthat an illustrative embodiment of the subject matter described hereinapplies regardless of the particular type of signal bearing medium usedto actually carry out the distribution. Examples of a signal bearingmedium include, but are not limited to, the following: a recordable typemedium such as a floppy disk, a hard disk drive, a Compact Disc (CD), aDigital Video Disk (DVD), a digital tape, a computer memory, etc.; and atransmission type medium such as a digital and/or an analogcommunication medium (e.g., a fiber optic cable, a waveguide, a wiredcommunications link, a wireless communication link, etc.).

In a general sense, those skilled in the art will recognize that thevarious aspects described herein which can be implemented, individuallyand/or collectively, by a wide range of hardware, software, firmware, orany combination thereof can be viewed as being composed of various typesof “electrical circuitry.” Consequently, as used herein “electricalcircuitry” includes, but is not limited to, electrical circuitry havingat least one discrete electrical circuit, electrical circuitry having atleast one integrated circuit, electrical circuitry having at least oneapplication specific integrated circuit, electrical circuitry forming ageneral purpose computing device configured by a computer program (e.g.,a general purpose computer configured by a computer program which atleast partially carries out processes and/or devices described herein,or a microprocessor configured by a computer program which at leastpartially carries out processes and/or devices described herein),electrical circuitry forming a memory device (e.g., forms of randomaccess memory), and/or electrical circuitry forming a communicationsdevice (e.g., a modem, communications switch, or optical-electricalequipment). Those having skill in the art will recognize that thesubject matter described herein may be implemented in an analog ordigital fashion or some combination thereof.

All of the above U.S. patents, U.S. patent application publications,U.S. patent applications, foreign patents, foreign patent applicationsand non-patent publications referred to in this specification and/orlisted in any Application Data Sheet, are incorporated herein byreference, to the extent not inconsistent herewith.

One skilled in the art will recognize that the herein describedcomponents (e.g., steps), devices, and objects and the discussionaccompanying them are used as examples for the sake of conceptualclarity and that various configuration modifications are within theskill of those in the art. Consequently, as used herein, the specificexemplars set forth and the accompanying discussion are intended to berepresentative of their more general classes. In general, use of anyspecific exemplar herein is also intended to be representative of itsclass, and the non-inclusion of such specific components (e.g., steps),devices, and objects herein should not be taken as indicating thatlimitation is desired.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations are not expressly set forth herein for sakeof clarity.

While particular aspects of the present subject matter described hereinhave been shown and described, it will be apparent to those skilled inthe art that, based upon the teachings herein, changes and modificationsmay be made without departing from the subject matter described hereinand its broader aspects and, therefore, the appended claims are toencompass within their scope all such changes and modifications as arewithin the true spirit and scope of the subject matter described herein.Furthermore, it is to be understood that the invention is defined by theappended claims. It will be understood by those within the art that, ingeneral, terms used herein, and especially in the appended claims (e.g.,bodies of the appended claims) are generally intended as “open” terms(e.g., the term “including” should be interpreted as “including but notlimited to,” the term “having” should be interpreted as “having atleast,” the term “includes” should be interpreted as “includes but isnot limited to,” etc.). It will be further understood by those withinthe art that if a specific number of an introduced claim recitation isintended, such an intent will be explicitly recited in the claim, and inthe absence of such recitation no such intent is present. For example,as an aid to understanding, the following appended claims may containusage of the introductory phrases “at least one” and “one or more” tointroduce claim recitations. However, the use of such phrases should notbe construed to imply that the introduction of a claim recitation by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim recitation to inventions containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should typically be interpreted to mean “atleast one” or “one or more”); the same holds true for the use ofdefinite articles used to introduce claim recitations. In addition, evenif a specific number of an introduced claim recitation is explicitlyrecited, those skilled in the art will recognize that such recitationshould typically be interpreted to mean at least the recited number(e.g., the bare recitation of “two recitations,” without othermodifiers, typically means at least two recitations, or two or morerecitations). Furthermore, in those instances where a conventionanalogous to “at least one of A, B, and C, etc.” is used, in generalsuch a construction is intended in the sense one having skill in the artwould understand the convention (e.g., “a system having at least one ofA, B, and C” would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). In those instances where aconvention analogous to “at least one of A, B, or C, etc.” is used, ingeneral such a construction is intended in the sense one having skill inthe art would understand the convention (e.g., “a system having at leastone of A, B, or C” would include but not be limited to systems that haveA alone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

With respect to the appended claims, those skilled in the art willappreciate that recited operations therein may generally be performed inany order. Examples of such alternate orderings may include overlapping,interleaved, interrupted, reordered, incremental, preparatory,supplemental, simultaneous, reverse, or other variant orderings, unlesscontext dictates otherwise. With respect to context, even terms like“responsive to,” “related to,” or other past-tense adjectives aregenerally not intended to exclude such variants, unless context dictatesotherwise.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to those skilled in the art.The various aspects and embodiments disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims.

1. An electromagnetic apparatus, comprising: a negatively-refractivefocusing structure disposed to receive electromagnetic energy in aninterior focusing region with an axial magnification substantially lessthan one.
 2. The electromagnetic apparatus of claim 1, furthercomprising: at least one electromagnetic sensor positioned within theinterior focusing region.
 3. The electromagnetic apparatus of claim 1,wherein the negatively-refractive focusing structure is disposed toreceive electromagnetic energy from an exterior field region.
 4. Theelectromagnetic apparatus of claim 3, wherein the axial magnificationcorresponds to a ratio of an axial extent of the interior focusingregion to an axial extent of the exterior field region.
 5. Theelectromagnetic apparatus of claim 1, wherein the negatively-refractivefocusing structure is characterized by electromagnetic parameters thatinclude: axial electromagnetic parameters; and transverseelectromagnetic parameters that inversely correspond to the axialelectromagnetic parameters.
 6. The electromagnetic apparatus of claim 5,wherein the electromagnetic parameters define a negative index ofrefraction within at least a portion of the interior focusing region. 7.The electromagnetic apparatus of claim 5, wherein the electromagneticparameters define an index of refraction less than minus one within atleast a portion of the interior focusing region.
 8. The electromagneticapparatus of claim 5, wherein the negatively-refractive focusingstructure defines an axial direction, and the axial electromagneticparameters correspond to the axial direction.
 9. The electromagneticapparatus of claim 8, wherein the transverse electromagnetic parameterscorrespond to a transverse direction, the transverse direction beingsubstantially perpendicular to the axial direction.
 10. Theelectromagnetic apparatus of claim 5, wherein the axial electromagneticparameters include an axial permittivity.
 11. The electromagneticapparatus of claim 10, wherein the transverse electromagnetic parametersinclude a transverse permittivity that is substantially a multiplicativeinverse of the axial permittivity.
 12. The electromagnetic apparatus ofclaim 11, wherein the axial permittivity is less than zero and greaterthan minus one.
 13. The electromagnetic apparatus of claim 10, whereinthe axial electromagnetic parameters include an axial permeability. 14.The electromagnetic apparatus of claim 13, wherein the transverseelectromagnetic parameters include a transverse permeability that issubstantially a multiplicative inverse of the axial permeability. 15.The electromagnetic apparatus of claim 14, wherein the axialpermeability is less than zero and greater than minus one.
 16. Theelectromagnetic apparatus of claim 13, wherein the axial permittivity issubstantially equal to the axial permeability.
 17. The electromagneticapparatus of claim 16, wherein the transverse electromagnetic parametersinclude a transverse permeability that is substantially a multiplicativeinverse of the axial permeability.
 18. The electromagnetic apparatus ofclaim 17, wherein the axial permeability is less than zero and greaterthan minus one.
 19. The electromagnetic apparatus of claim 1, whereinthe negatively-refractive focusing structure includes an input surfaceregion that is substantially nonreflective of electromagnetic energyincident upon the input surface region.
 20. The electromagneticapparatus of claim 19, wherein the input surface region is substantiallynonreflective of electromagnetic energy incident upon the input surfaceregion from an adjacent region, the adjacent region being exterior tothe negatively-refractive focusing structure.
 21. The electromagneticapparatus of claim 20, wherein a wave impedance of the adjacent regionis substantially equal to a wave impedance of the input surface region.22. The electromagnetic apparatus of claim 21, wherein the adjacentregion defines a first permittivity and a first permeability, the inputsurface region defines a second permittivity and a second permeability,and a ratio of the second permittivity to the first permittivity issubstantially equal to a ratio of the second permeability to the firstpermeability.
 23. The electromagnetic apparatus of claim 22, wherein thesecond permittivity is less than zero.
 24. The electromagnetic apparatusof claim 22, wherein the second permeability is less than zero.
 25. Theelectromagnetic apparatus of claim 24, wherein the second permittivityis less than zero.
 26. The electromagnetic apparatus of claim 22,wherein the input surface region defines a surface normal direction anda surface parallel direction, the second permittivity includes a surfacenormal permittivity corresponding to the surface normal direction and asurface parallel permittivity corresponding to the surface paralleldirection, and a ratio of the surface normal permittivity to the firstpermittivity is substantially a multiplicative inverse of a ratio of thesurface parallel permittivity to the first permittivity.
 27. Theelectromagnetic apparatus of claim 26, wherein the ratio of the surfacenormal permittivity to the first permittivity is less than zero andgreater than minus one.
 28. The electromagnetic apparatus of claim 26,wherein the second permeability includes a surface normal permeabilitycorresponding to the surface normal direction and a surface parallelpermeability corresponding to the surface parallel direction, and aratio of the surface normal permeability to the first permeability issubstantially a multiplicative inverse of a ratio of the surfaceparallel permeability to the first permeability.
 29. The electromagneticapparatus of claim 28, wherein the ratio of the surface normalpermittivity to the first permittivity is less than zero and greaterthan minus one.
 30. The electromagnetic apparatus of claim 1, whereinthe negatively-refractive focusing structure includes anartificially-structured material having an effective electromagneticresponse that corresponds to the electromagnetic parameters.
 31. Theelectromagnetic apparatus of claim 30, wherein the interior focusingregion is at least partially inside the artificially-structuredmaterial.
 32. The electromagnetic apparatus of claim 31, wherein theinterior focusing region is completely inside theartificially-structured material.
 33. The electromagnetic apparatus ofclaim 30, wherein the artificially-structured material includes aphotonic crystal.
 34. The electromagnetic apparatus of claim 30, whereinthe artificially-structured material includes a metamaterial.
 35. Theelectromagnetic apparatus of claim 34, wherein the metamaterial includesat least one electromagnetically-responsive structure having a pluralityof distributed electromagnetic responses, the plurality of distributedelectromagnetic responses composing the effective electromagneticresponse.
 36. The electromagnetic apparatus of claim 35, wherein thedistributed electromagnetic responses include distributed inductiveresponses.
 37. The electromagnetic apparatus of claim 35, wherein thedistributed electromagnetic responses include distributed capacitiveresponses.
 38. The electromagnetic apparatus of claim 35, wherein thedistributed electromagnetic responses include distributedinductive-capacitive responses.
 39. The electromagnetic apparatus ofclaim 35, wherein the at least one electromagnetically-responsivestructure includes transmission lines.
 40. The electromagnetic apparatusof claim 34, wherein the metamaterial includes a plurality ofelectromagnetically responsive elements disposed at a plurality ofspatial locations and having a plurality of individual responses, theplurality of individual responses composing the effectiveelectromagnetic response.
 41. The electromagnetic apparatus of claim 40,wherein the electromagnetically responsive elements include discretecircuit elements.
 42. The electromagnetic apparatus of claim 41, whereinthe discrete circuit elements include inductors.
 43. The electromagneticapparatus of claim 41, wherein the discrete circuit elements includecapacitors.
 44. The electromagnetic apparatus of claim 41, wherein thediscrete circuit elements include semiconductor devices.
 45. Theelectromagnetic apparatus of claim 44, wherein the semiconductor devicesinclude diodes.
 46. The electromagnetic apparatus of claim 44, whereinthe semiconductor devices include transistors.
 47. The electromagneticapparatus of claim 40, wherein the electromagnetically responsiveelements include integrated circuit elements.
 48. The electromagneticapparatus of claim 40, wherein the electromagnetically responsiveelements include printed circuit elements.
 49. The electromagneticapparatus of claim 40, wherein the electromagnetically responsiveelements include metallic structures.
 50. The electromagnetic apparatusof claim 40, wherein the electromagnetically responsive elements includeLC resonators.
 51. The electromagnetic apparatus of claim 40, whereinthe electromagnetically responsive elements include plasmonicresonators.
 52. The electromagnetic apparatus of claim 40, wherein theelectromagnetically responsive elements include nanostructures.
 53. Theelectromagnetic apparatus of claim 52, wherein the nanostructuresinclude nanorods.
 54. The electromagnetic apparatus of claim 53, whereinthe nanorods are paired nanorods.
 55. The electromagnetic apparatus ofclaim 53, wherein the nanorods are interconnected to compose a fishnetstructure.
 56. The electromagnetic apparatus of claim 40, wherein theelectromagnetically responsive elements include split-ring resonators.57. The electromagnetic apparatus of claim 40, wherein theelectromagnetically responsive elements include subwavelength elementshaving spatial extents substantially less than a free space wavelengthcorresponding to a frequency of the electromagnetic energy.